Real Analysis, Lecture 5: Complex Numbers

[@dopplerdog6817]

I'll stop him from "doing that" if no one else will. The absolute madman must be stopped.

[@emilyla6415]

"You can't stop me from making a definition like this"

[@bluestarrfall]

around 36:11 - jumping mathematician. Love this lecture series! :)

[@56jmoney]

@58:08 Yes you are missing something on the right hand side. The length of the complex number v, expressed as a dot product, is The same for the length of w.

[@AnlamK]

He says they are real.

[@adamlevy1845]

Actually the lecturer is correct. In Bra Ket notation the first quantity in the bracket is complex-conjugated before being dotted with the second quantity.

[@aravindgundakaram1830]

Uhhhh, he is using the bra ket notation, so he is correct.

[@ldb579932]

At 59:20 "times the sine of the angle between" should be "the cosine of the angle between"

[@nirbhayonline]

what great humanity towards mankind..

[@aravindgundakaram1830]

Idk why but I get the impression that you are in confusion my man

[@SequinBrain]

forgetting my dots & crosses, I don't remember why there's a negative bd, then a positive bc for xy. I remember i, j, k, but this isn't that.

[@darksecret965]

it's not related to dot or cross prods, it's the multiplication of complex numbers. essentially the negative sign comes from i^2 = -1, or in other words, multiplying imaginary parts gets you a negative real part

[@SequinBrain]

@@darksecret965 yeah, i, j, and k are imaginary. thx

[@kazifamily8042]

51:12 the triangle inequality. The CS Inequality.

[@buddygordy3253]

Is there anywhere we can get a less blurry version of this? Sometimes it is hard to read.

[@itsssssssu2086]

Press the Cc button there will be subtitles 👀

[@SACCst]

@@itsssssssu2086brilliant

[@ShokoDemon]

YOU CAN'T STOP ME. *spins like the mask throwing symbols around* WEEEEEE

[@elidrissii]

Cross that. There wouldn't be Physics if it weren't for Math. Do you really think Classical Physics would have existed without the use of Calculus? Sure people could have realized that bodies accelerate downwards, but it wouldn't go one inch further.

[@thbeam2044]

36:16 i hope to one day be on this level.

[@peter_castle]

Maybe they would be anti-matter apples.

[@beback_]

A vecTOR

[@hcoetze]

if a have i apples, what would that look like?

[@beback_]

H.A. Coetzee I believe complex numbers don’t correspond meaningfully with any notion of counting or measurement. As far as I know they just make solving differential equations and whatnot easier.

[@rampadmanabhan4258]

@@beback_ Think this is related to the fact that the complex field does not have order.

[@TheStraightThinker]

Math is what gives structure and the foundation for all sciences, without math physics would be a bunch of interesting but impractical theory.

[@kylepoe5139]

What a vacuous statement

[@abelvictor8322]

Jeez, I really wanted to stop him from calling (0,1) "i"

[@htmos]

And by the way wouldn't it be more fair to call it Cauchy-Bunyakovsky-Schwarz inequality?

[@wiseguy459]

Isn't it slightly distracting when they keep looking at their notes every two minutes?

[@wiseguy459]

+Supreeth Ravish Also, the whispering.

[@beback_]

Nah

[@milksushi6640]

Filmed with a potato, recorded with a banana.

[@x0cx102]

It's 2010 what'd you expect idiot

[@victorserras]

Wonder why he'd spend almost 40 minutes talking about Complex things in a Real Analysis course..

[@emlmm88]

Victor Serra They're relevant to functions of real variables. You'll see.

[@TehFingergunz]

comma, comma, comma, chameleon... kek

[@sahilguleria4979]

💌thank you

[@austinisi]

lol @ 44:53

[@htmos]

I know for sure that the Universe would exist without mankind (and their ideas, calculus etc.).

[@emeliseabdaal8240]

What the fuck? I'm doing this in high school.

[@Fematika]

It's quite simple.

[@htmos]

Good lecture, but there's something I did not like: "Cauchy inequality is the basis for the Heisenberg principle..." Heisenberg principle or anything else is physics is not a consequence of some math manipulations, OK?

[@krajco252]

i dont thing he is a good teacher

[@sahilguleria4979]

Why